A modified Wiener-type filter for geodetic estimation problems with non-stationary noise |
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Authors: | C Kotsakis M G Sideris |
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Institution: | (1) Department of Geodesy and Surveying, Faculty of Engineering, Aristotle University of Thessaloniki, Univ. Box 440, Thessaloniki 540 06, Greece; e-mail: kotsakis@alumni.ucalgary.ca; Fax: +30-31-995948, GR;(2) Department of Geomatics Engineering, University of Calgary, 2500 University Drive NW, Calgary T2N 1N4, Alberta, Canada; e-mail: sideris@ucalgary.ca; Fax: +1-403-2841980, CA |
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Abstract: | One of the most basic and important tools in optimal spectral gravity field modelling is the method of Wiener filtering.
Originally developed for applications in analogue signal analysis and communication engineering, Wiener filtering has become
a standard linear estimation technique of modern operational geodesy, either as an independent practical tool for data de-noising
in the frequency domain or as an integral component of a more general signal estimation methodology (input–output systems
theory). Its theoretical framework is based on the Wiener–Kolmogorov linear prediction theory for stationary random fields
in the presence of additive external noise, and thus it is closely related to the (more familiar to geodesists) method of
least-squares collocation with random observation errors. The main drawback of Wiener filtering that makes its use in many
geodetic applications problematic stems from the stationarity assumption for both the signal and the noise involved in the
approximation problem. A modified Wiener-type linear estimation filter is introduced that can be used with noisy data obtained
from an arbitrary deterministic field under the masking of non-stationary random observation errors. In addition, the sampling
resolution of the input data is explicitly taken into account within the estimation algorithm, resulting in a resolution-dependent
optimal noise filter. This provides a more insightful approach to spectral filtering techniques for noise reduction, since
the data resolution parameter has not been directly incorporated in previous formulations of frequency-domain estimation problems
for gravity field signals with discrete noisy data.
Received: 1 November 2000 / Accepted: 19 June 2001 |
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Keywords: | : Wiener filter – Non-stationary noise – Data resolution – Translation-invariant estimation – Fast Fourier transform |
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